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Possible contribution of quantum-like correlations to the placebo effect: consequences on blind trials

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Background. Factors that participate in the biological changes associated with a placebo are not completely understood. Natural evolution, mean regression, concomitant procedures and other non specific effects are well-known factors that contribute to the “placebo effect”. In this article, we suggest that quantum-like correlations predicted by a probabilistic modeling could also play a role. Results. An elementary experiment in biology or medicine comparing the biological changes associated with two placebos is modeled. The originality of this modeling is that experimenters, biological system and their interactions are described together from the standpoint of a participant who is uninvolved in the measurement process. Moreover, the small random probability fluctuations of a “real” experiment are also taken into account. If both placebos are inert (with only different labels), common sense suggests that the biological changes associated with the two placebos should be comparable. However, the consequence of this modeling is the possibility for two placebos to be associated with different outcomes due to the emergence of quantum-like correlations. Conclusion. The association of two placebos with different outcomes is counterintuitive and this modeling could give a framework for some unexplained observations where mere placebos are compared (in some alternative medicines for example). This hypothesis can be tested in blind trials by comparing local vs. remote assessment of correlations.
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R E S E A R C H Open Access
Possible contribution of quantum-like
correlations to the placebo effect:
consequences on blind trials
Francis Beauvais
Correspondence:
beauvais@netcourrier.com
91, Grande Rue, Sèvres, France
Abstract
Background: Factors that participate in the biological changes associated with a
placebo are not completely understood. Natural evolution, mean regression,
concomitant procedures and other non specific effects are well-known factors that
contribute to the placebo effect. In this article, we suggest that quantum-like
correlations predicted by a probabilistic modeling could also play a role.
Results: An elementary experiment in biology or medicine comparing the biological
changes associated with two placebos is modeled. The originality of this modeling is
that experimenters, biological system and their interactions are described together
from the standpoint of a participant who is uninvolved in the measurement process.
Moreover, the small random probability fluctuations of a realexperiment are also
taken into account. If both placebos are inert (with only different labels), common
sense suggests that the biological changes associated with the two placebos should
be comparable. However, the consequence of this modeling is the possibility for two
placebos to be associated with different outcomes due to the emergence of
quantum-like correlations.
Conclusion: The association of two placebos with different outcomes is
counterintuitive and this modeling could give a framework for some unexplained
observations where mere placebos are compared (in some alternative medicines for
example). This hypothesis can be tested in blind trials by comparing local vs. remote
assessment of correlations.
Keywords: Placebo effect, Quantum-like correlations, Experimenter effect,
Randomized clinical trials
Background
Much has been written about the placebo effectand the purpose of this article is not
to make a review on this topic [16]. In itself the term placebo effectis curious and
paradoxical. Indeed, as underscored by Moerman and Jonas: The one thing of which
we can be absolutely certain is that placebos do not cause placebo effects. Placebos are
inert and dont cause anything[1]. For this reason, Ernst and Resch insisted to clarify
the definition of placebo by distinguishing perceived placebo effectand true placebo
effect[7]. Perceived placebo effect is the outcome that is associated with the placebo
group in a trial; it includes natural evolution of the disease, mean regression, concomi-
tant procedures and other non specific effects. True placebo effect is the difference
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publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
Beauvais Theoretical Biology and Medical Modelling (2017) 14:12
DOI 10.1186/s12976-017-0058-5
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
between perceived placebo effect and effect associated with no treatment. No
treatmentgroups are however infrequently performed and therefore there are often
some misunderstandings to define the scope of the placebo effect.
Since placebos are inert, the causes of the true placebo effectshould be sought ra-
ther on the side of language and psychology. Thus, it has been shown that placebo ef-
fects can be caused by cognitive and emotional changes, expectation of symptom
changes or classical conditioning [2]. Actual effects of placebo on brain and body have
been evidenced and there are neurobiological underpinnings for these effects [8, 9].
However, in most studies aimed to decipher the placebo effect, patients are at the
centre of the investigations and all explanations rest on them. In the present article, the
experimental design and the experimenters are also taken into consideration. There-
fore, the focus is moved from patients to investigators and in this case the placebo
effect at least one of its components is not much different than an experimenters
effect. A famous example of experimenters effect was evidenced in the experiments of
Rosenthal et al. where an experimenter obtained from his subjects the data he expected
or wanted to obtain [10]. Outside of psychology, for example in cell biology or in physi-
ology, it is generally thought that such subtle influences could not be responsible for re-
sponse biases. In clinical trials, blind experiments are supposed to protect against any
outcome bias related to patient or physician; if such influences exist, they are distrib-
uted randomly in test and placebo groups. In the present article, it is suggested that
quantum-like correlations predicted by a probabilistic modeling could also contribute
to the placebo effect.
Results
Design of a minimal experiment with two placebos
The purpose of a typical experiment in medicine or biology is to establish a relationship
between a cause(independent variable) and a biological effect. Placebos (or
controlsin experimental biology) are included in the experiment in order to assess
the effects of variables other than the independent variable.
We define a biological object(biological model or patients in a clinical trial) with
two possible states: no biological change (or resting state, not different from back-
ground noise) and biological change (activatedstate). A biological change may be de-
fined by setting a cut-off value of a continuous variable. We symbolize no biological
change as and biological change as .
We assume that all samples that are tested are placebos and that the only difference
is their labels which are either Pcb
0
or Pcb
1
. Since samples are all inert and physically
identical, common sense suggests that the biological outcomes associated with the two
placebos should be comparable. Nevertheless, the aim of the modeling is to know
whether in some circumstances the state could be more frequently observed with
one of the two labels (no matter which one at this stage). Therefore, the null hypothesis
(H
0
) of such an experiment is:
H0:Prob jPcb0
ðÞ¼Prob jPcb1
ðÞ ð1Þ
Prob (xy) is the conditional probability of xgiven y(or the probability of xunder
the condition y).
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Figure 1 describes the two possible relationships between labels and biological out-
comes: either directrelationship (Pcb
0
associated with and Pcb
1
associated with
)orreverserelationship (Pcb
0
associated with and Pcb
1
associated with ).
Note that this naming (director reverse) is arbitrary and does not prejudge results.
Of course, if a biological change is associated with the labels Pcb
0
and Pcb
1
with the
same rate (i.e. no relationship), then the probabilities of direct and reverse relation-
ship are both equal to 1/2. By convention, we present calculations of probability mainly
for direct relationship (the sum of the probabilities of direct and reverse relationships is
equal to one).
Description of an experiment from an uninvolved standpoint
The originality of the present modeling is that observers, observed system and their in-
teractions are described together from an uninvolved standpoint. The formalism is in-
spired from the relational interpretation of quantum physics [11, 12] and quantum
Bayesianism (QBism) [13, 14].
We suppose that the experimental landscape is described by a participant who is
uninvolved in the experiment. Suppose,asdescribedinFig.2,anobserverOwho
measures a variable of a system S; this variable can take one of the two values
leftand rightafter a measurement. For a participant Puninvolved in the meas-
urement process, a definite value has been obtained after the measurement of Sby
O(either leftor right). Pknows that O has observed a defined value after
measurement, but Pdoes not know what O has observed. If Pfinally observes the
system S, he records a definite value and he agrees with Oon this value when P
and Ointeract. Interactions between observers are like measurements and they
allow establishing correlations.
In this last case, it is important to underscore that it is not correct to say that Pis
forcedto observe what Oobserved before they interact. Indeed, one can imagine an-
other participant Qwho in turn describes S,Oand Pwithout interacting with them.
What Qcan say is that a correlation has been established between S,Oand P, but Q
Fig. 1 Relationships between placebos and biological system. There are two possible placebos (0and 1)
and two possible states for the biological system: no change (restingstate or background) which is noted
and biological change above background (activatedstate) which is noted . As a consequence, there
are two possible relationships defined as: direct relationship with placebo 0associated with and
placebo1 associated with ; reverse relationship with placebo 0associated with and placebo 1
associated with
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cannot say which result is observed. The only thing that an uninvolved participant can
do is to describe the form (correlations), but not the content (outcomes) of the informa-
tion available to the observers who interact with Sand with each other. Thus, the
consistency of any measurement is guaranteed.
Note that, strictly speaking, an uninvolved participant does not describe the reality
itself (made of contents), but he constructs a predictive tool (made of correlations
and probabilities) in order to know what to expect if he decides to interact with the
realobservers.
Probabilistic modeling of a minimal experiment with two placebos
An experiment is modeled from the standpoint of a participant Pwho is outside the la-
boratory, as described in the previous section. The participant Pdoes not interact with
the objectsthat he describes and he remains uninvolved in the evolution of the ex-
perimental situation. The role of Pis to describe the evolution of a team of interacting
experimenters with the knowledge of the initial conditions.
We consider a team composed of two experimenters named Oand Owho observe
the biological system S. We suppose an experimental situation where the probability
for each experimenter to observe a direct relationship (as defined in Fig. 1) is pand the
probability of a reverse relationship is q(with p+q= 1).
Each observer has his own probabilistic expectations and the uninvolved participant
Passigns the probability pto Oas the best estimate that Ocan make for the future ob-
servation of the direct relationship. The same probability pis assigned to Oindepend-
ently of Osince the probabilistic expectations are specific to each observer.
Fig. 2 Description of an experiment from an uninvolved standpoint. The observer Omeasures the system
Swhereas the participant Premains uninvolved in the measurement (he does not interact with Oand S).
Pknows that Ohas observed a definite state of S, but he does not know which one. If Pfinally interacts
with Oand S, then Pand Oagree on the outcome of S. The reasoning can be continued with another
participant Qwho does not interact with S,Oand P. What Qcan say is that S,Oand Phave definite values
that are correlated. The only thing that an uninvolved participant can do is to describe the form, but not
the content of the information available to the observers who interact with Sand with each other. Thus,
the consistency of any measurement is guaranteed (GNU Free Documentation License)
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Therefore, the participant Pconstructs a predictive tool for his own use where the ex-
perimenters have independent probabilistic expectations on the experimental outcome
and are in agreement when they compare their records. The future outcome that Oex-
pects to record (event A) and the future outcome that Oexpects to record (event B)
are independent events in the probability space constructed by P(Fig. 3). This condi-
tion of independence is easily formalized since the probabilities of two independent
events Aand Bhave well-known mathematical properties:
Prob ABðÞ¼Prob AðÞProb BðÞ ð2Þ
Therefore, when Oand Ointeract and agree on the result of the experiment (i.e. the
events of the set AB), the best estimate of the probability that Oand Oobserve a
direct relationship is Prob (direct)=p×paccording to Eq. (2) since the probability to
record a direct relationship was estimated to be pfor Oand also pfor O(Fig. 3). Simi-
larly, the best estimate of the probability that Oand Oobserve a reverse relationship is
Prob (reverse)=q×q.
The intersubjective agreement discards some impossible situations such as Oobserves
a direct relationship while Oobserves a reverse relationship. Since the sum of the prob-
abilities of all possible events is equal to one, Prob (direct)=p×pmust be renormalized.
For this purpose, p×pis divided by the sum of the probabilities of all possible outcomes
(grey areas in Fig. 3), namely direct relationship (p×p) and reverse relationship (q×q):
Prob directðÞ¼
p2
p2þq2ð3Þ
Fig. 3 Probabilistic space constructed by an uninvolved participant Pto predict the outcomes of the
experiments. A team of interacting experimenters Oand Ois described from the standpoint of an uninvolved
participant who knows the initial experimental conditions (Fig. 2). We suppose a probability equal to pfor the
event direct relationshipand equal to qfor the event reverse relationship(p+q= 1). Each observer has his
own probabilistic expectations and Passigns the probability pto Oas the best estimate that Ocan make for
the future observation of a direct relationship; the same probability is assigned to Oindependently of Osince
the probabilistic expectations are specific to each observer. White areas are unauthorized experimental
situations with incompatible outcomes after interaction of Oand O(e.g. directfor Oand reversefor O).
Therefore, the probability that the experimenters observe a direct relationship is calculated by dividing the
central gray area (directfor both observers) by the sum of the probabilities of possible outcomes (either
director reversefor both observers), namely all gray areas. Ω, probability space
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By dividing both the numerator and the denominator by p
2
(taking into account that
p+q= 1), the only variable of the equation is p:
Prob directðÞ¼ 1
1þ1
p1

2ð4Þ
Eqs. (3), (4) and Fig. 3 are easily generalized to any number Nof observers who all
agree on the outcome:
Prob directðÞ¼ 1
1þ1
p1

Nð5Þ
In a realexperiment, particularly in biology, random fluctuations occur and they
must be taken into account because, after each elementary fluctuation, a tiny bias is in-
troduced and Prob (direct) must be updated.
In the next lines we calculate the evolution of the probability for Oand Oto observe a
direct relationship from the standpoint of the participant P. First, we write that Prob
(direct) is equal to 1/2 in the absence of observers (N= 0 in Eq. (5)). As a consequence,
the initial value of Prob (direct)attimet
0
before the first fluctuation is equal to p
0
=1/2.
We then introduce ε
i
as successive elementary random fluctuations of Prob (direct)
that occur during successive elementary intervals of time (ε
i
are positive or negative
real random numbers such as ε
i
< < 1). Note that an implicit consequence of the ran-
dom fluctuations of Prob (direct) is a non-null, but very small, probability to observe a
biological change ().
After the first fluctuation ε
1
, we easily calculate with Eq. (4) the updated probability
p
1
which is based on p
0
+ε
1
. The equation is then generalized for any probability p
n+1
based on previous probability p
n
and fluctuation ε
n+1
. We obtain a mathematical se-
quence which allows calculating the successive probabilities of a direct relationship:
Probnþ1ðdirectÞ¼pnþ1¼1
1þ1
pnþεnþ11

Nwith p0¼1=2ð6Þ
Two placebos associated with different outcomes
Equation 6 allows calculating the successive states of a system constituted of a bio-
logical system and a team of interacting experimenters/observers committed in the es-
tablishment of a supposed relationship.
A computer calculation of this mathematical sequence is described in Fig. 4 after 100
successive random fluctuations ε
i
(with values around 10
15
) and with two observers
(N= 2). We observe that the initial situation is in fact metastable if fluctuations are
taken into account. Indeed, in all cases (i.e. whatever the series of values ε
i
), a dramatic
transition towards one of two stable positions is achieved:
Prob ðdirectÞ¼1=2ðmetastable positionÞ
Prob ðdirectÞ¼1or 0ðtwo possible stable positionsÞ
ð7Þ
All samples of an experiment are thus engaged either in a direct relationship or in a
reverse relationship. Note that the probability of a biological change was very small
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initially and, after the transition, a biological change is systematically associated with
the label Pcb
1
in stable position #1 or systematically associated with the label Pcb
0
in
stable position #2. The choice of one of the two stable positions is random. In both
cases, a relationship (direct or reverse) between labels and outcomes emerges.
However, the purpose of an experiment is to compare a testsituation with a
controlsituation. Biological systems are therefore prepared in an asymmetrical state
with resting state (background noise) implicitly associated with a controlsituation.
The stability of the resting state (or basic state) is a condition for a proper assessment
of the samples (the experiment begins with the preparation of the biological system be-
fore samples are tested). In other terms, the state of the biological model at rest (before
each test) can be considered as associated with the label control.
We suppose, for example, that Pcb
0
is considered as a controlby the experimenters.
Consequently the stable state #2 eliminates itself since Pcb
0
cannot be associated both
with change (when Pcb
0
samples are tested) and with no change (for the resting state).
Only the stable position #1 is a possible state:
Prob ðdirectÞ¼1=2ðmetastable positionÞ
Prob ðdirect Þ¼1ðstable positionÞ
ð8Þ
A probability equal to one for the direct relationship means that the participant Pis
assured if he finally interacts with the team of experimenters after the end of the
experiment to observe a direct relationship between labels and biological outcomes.
Thanks to probability fluctuations, a biological change associated with each sample
with Pcb
1
label emerges from background noise.
Fig. 4 Calculation of the probability of a direct relationship. The evolution of the probability that a team
(composed of two members who interact) observes a direct relationship is described in this figure by taking
into account successive probability fluctuations. The probability defined in Fig. 3 is calculated according to
the mathematical sequence in the cartouche. Each successive probability p
n+1
of the sequence is calculated
by using p
n
and a random probability fluctuation is randomly obtained between 0.5 and +0.5 × 10
-15
. This
computer simulation shows that the initial state with a probability of 1/2 is in fact metastable and, after a
dramatic transition, one of two stable positions is achieved: either Prob (direct) = 1 or Prob (direct) = 0. With
N> 2 or with higher values of probability fluctuations, a transition is obtained after a lower number of
calculation steps (data not shown). Eight computer simulations are reported in this figure
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Consequences of different types of blind designs on correlations
Until now we examined an experimental situation where the observers Oand O
assessed themselves the rates of correlation between labels and biological outcomes
(open-label experiments). Nevertheless, the labels can be masked to the experi-
menters in order to reduce or eliminate any bias. After the outcomes have been
obtained in blind conditions for all samples, the labels of samples are unmasked.
In this article, we distinguish blind experiments with either local or remote assess-
ment of correlations.
For a local assessment of correlations with blind design, an automatic device or a
member of the team of experimenters keeps secret the labels of the samples until the
end of the experiment. In this case, the automatic device or the observer who is dedi-
cated to the blinding are also elements of the experiment because they interact with
the other observers and can be described (from the standpoint of P) with the same
modeling as open-label experiments.
A remote assessment of correlations with blind design is typically used in randomized
clinical trials (also named centralized blind design). The remote supervisor (a statisti-
cian for example) does not interact with the experimenters before all measurements are
completed. It is important to underscore that the remote supervisor should not be con-
fused with the uninvolved participant Pwho describes the experiment. Indeed, Pdoes
not interact and is not involved in the experiment. With a remote supervisor, the ex-
perimenters observe biological outcomes, but have no feedback on labels before the re-
mote experimenter is aware of the rate of success. As a consequence, Prob (direct)=
Prob (reverse); since Prob (direct) + Prob (reverse) = 1, then Prob (direct) = 1/2. In
summary:
Prob (direct) = 1 with local assessment of correlations;
Prob (direct) = 1/2 with remote assessment of correlations.
Figure 5 illustrates the consequences of the assessment of the correlations with a re-
mote assessment according to the modeling. In this case (blind experiment with an ex-
ternal supervisor), there is no statistical difference between the biological outcomes
associated with Pcb
0
and Pcb
1
in contrast with a local assessment (local blind design or
open-label experiment).
The experimental context is therefore crucial for establishing a relationship in
the modeling. With a local assessment, the experimenters observe labels and then
biological outcomes (open-label experiment) or observe biological outcomes and
then labels (local blind experiments). In contrast, with a remote supervisor, the ex-
perimenters observe biological outcomes, but have no feedback on labels. If a local
observer/experimenter is the first to assess the relationship, correlations emerge; if
a remote supervisor is the first to assess the relationship, correlations vanish (bio-
logical changes are nevertheless observed, but at random places). Of course, in all
cases, when participants met together, they agree on the conclusion (correlation or
no correlation). The order of the assessments (local first or remote first) is the key
element for the degree of correlation.
It is important to underscore that this difference between local and remote assess-
ment of correlations offers the opportunity to test the modeling.
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Characterization of the role of the observers O and O
The experimenters/observers Oand Oplay a crucial role in the modeling and we
examine in this section how their involvement could be characterized and quantified.
As previously reported in Eq. (2), the joint probability of two independent events A
and Bis equal to the product of the separate probabilities of Aand B. This equation
can be generalized for two events Aand Baccording to their degree of independence:
Prob ABðÞ¼Prob AðÞProb BðÞþdwith 0 d1ðÞ ð9Þ
The degree of independence increases when the value of ddecreases; the two events
are completely independent with d= 0. In other words, the correlation of the two
events increases when the value of dincreases. Eq. (3) can be easily modified if dis
taken into account (Fig. 6; see legend for calculation details):
Prob directðÞ¼
p2þd
p2þq2þ2dwith 0 dpqðÞ ð10Þ
When the parameter dvaries from d=pq to d= 0, the experimental situation pro-
gressively shifts from a classical description to the present modeling (Fig. 6).
Observingan experiment requires a frame (what are we expecting?) and a feedback
(what did we record?). Equation (6) indicates that there is no transition of Prob (direct)
towards a stable position in the absence of observers (N= 0). We can draw the same
conclusion if the observers are physically present in the laboratory, but not focusing
Fig. 5 Comparison of local vs. remote assessment in an experiment with two placebos. In an experiment with
a local assessment (local blind design or open-label experiment), correlations between labels (Pcb
0
and Pcb
1
)
and states of the biological system (and )emerge(band e) from the initial state (aand d). These correlations
vanish if the assessment of the experiment is made in a blind experiment with a remote supervisor (cand f). In
this latter case, the difference between the biological changes associated with Pcb
0
and Pcb
1
is not statistically
significant (NS) and the biological changes () are randomly distributed among the two placebos. The
difference of results in local vs. remote assessments offers the opportunity to test the modeling
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their attention on this specific experiment (they expect nothing about the experimental
system and they do not receive feedback). As a consequence, the parameter dcan be
considered as an evaluation of the attention of the team of experimenters to observe
the predefined relationship between labels and biological outcomes. When d= 0, the
observers are fully committed and for d=pq their attention is completely drawn away
from the experiment. For intermediate values, the team is more or less occupied with
these observations. Therefore, experimentersqualities, such as attention, commitment
and persistence, appear to be necessary during the experiments for the emergence of
correlations between labels and biological outcomes.
We can go a step further by considering that the parameter dis also an assess-
ment of the capability of the experimenters to recognize (or not) the direct and re-
verse relationships per se, i.e. as new objectsregardless their components, namely
the association of the biological outcomes with Pcb
0
and Pcb
1
. Indeed, in Eq. (4)
(i.e. with d= 0), it is implicit that the experimenters recognize the outcome per se
(i.e. in its wholenessor as such) as it would be the case for the outcome of a
dice roll or the position of a pointer on a measurement device. But suppose now a
team of experimenters Oand Owho are inexperienced and do not recognize the
predefined experimental relationship as a structured ensemble. The experimenters
identify the sub-events as separate elements without integrating them as a whole
(these sub-events are the association of the biological outcomes with Pcb
0
and
Pcb
1
). Since we continue to adopt the standpoint of P, we use Eq. (4) to calculate
the evolution of the probability of each sub-event. Before the first fluctuation prob-
ability, the probabilities of the two sub-events are: Prob (direct |Pcb
0
)=1 and Prob
(direct |Pcb
1
)=0(seeFig.5a).WenoticethatProb(direct |Pcb
0
) and Prob (direct |Pcb
1
)
are already in stable positions. Therefore, by using Eq. (4) (see also Fig. 4), these condi-
tional probabilities are maintained in their respective stable positions with Prob (direct |
Pcb
0
) that tends toward 1 and Prob (direct |Pcb
1
) that tends toward 0. The experimental
Fig. 6 From a classical description of the experimental situation to the present modeling. The experimental
situation depicted in Fig. 3 is generalized in this figure by using the parameter dwhich varies with the
degree of independence of the probabilistic expectations on the outcome assigned to Oand O. The values
of the two areas with impossible situations (direct relationship for one observer and reverse relationship for
the other one) are calculated as: p(p
2
+d)=(1 p)d=pq d. For d= 0, correlations between labels
and biological outcomes emerge and, for d=pq, the probability of a direct relationship is equal to pas in
classical probability. Ω, probability space
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results associated with these uncoupled sub-events can be gathered in order to calculate
Prob (direct) by using the law of total probability:
Prob directðÞ¼Prob Pcb0
ðÞProb directjPcb0
ðÞþProb Pcb1
ðÞ
Prob directjPcb1
ðÞ ð11Þ
¼1=21þ1=20¼1=2ð12Þ
As a consequence, because the relationship between labels and biological outcomes is
not recognized as a structured ensemble, there is no transition and Prob (direct) tends
toward 1/2.
These considerations are reminiscent from Gestalt psychology that states that human
mind spontaneously tends to perceive phenomena as structured ensembles (Gestalt)
and not as a simple addition of parts. For example, the well-known Necker cube is im-
mediately recognized as a 3D cube by a human observer and not as the simple addition
of lines drawn on a 2D sheet [15]. We instantly seea cube in space because we have
learned to perceive these 2D drawings as 3D objects.
As for Necker cube, cognitive and learning processes are undoubtedly at work for the
passage from an analytic(d=pq)toastructured(or global) perspective (d= 0). In
the first situation (d=pq), the experimenters are spectators of the experimental landscape
that is perceived as a collection of points;inthesecondsituation(d= 0), they are actors
who interpret the experimental landscape that is perceived as a form[15]. In this last case,
the experimenters concentrate their attention towards a transcendent object(namely, the
predefined relationship) without reference to the details that become indiscernible.
If cognitive and learning processes are involved in the emergence of quantum-like
correlations, different teams of experimenters with different training and experience
should report various degrees of correlations between labels and biological outcomes in
experiments comparing two placebos.
Emergence of a quantum-like logic
Only tools from classic probability are used in the modeling. Nevertheless, as demon-
strated in this section, there is an underlying quantum-like logic which is rooted in the
initial partition of placebos as Pcb
0
and Pcb
1
. Indeed, according to Fig. 1:
Prob Pcb0
ðÞProb ðÞþProb Pcb0
ðÞProb ðÞþProb Pcb1
ðÞProb ðÞ
þProb Pcb1
ðÞProb ðÞ¼1:
ð13Þ
When the stable position #1 is achieved, Prob (Pcb
0
) = Prob () and Prob (Pcb
1
)=
Prob () (see Fig. 5b); when the stable position #2 is achieved, Prob (Pcb
0
) = Prob ()
and Prob (Pcb
1
) = Prob (). Therefore in both cases:
Prob Pcb0
ðÞ½
2þProb Pcb1
ðÞ½
2þ2Prob Pcb0
ðÞProb Pcb1
ðÞ¼1ð14Þ
This equation is equivalent to:
Prob Pcb0
ðÞþProb Pcb1
ðÞ½
2¼1ð15Þ
Then, we define aand bsuch as Prob (Pcb
0
)=a
2
(or a.a)andProb(Pcb
1
)=b
2
(or b.b). These definitions correspond to the stable position #1 (for the stable pos-
ition #2, b
2
must be taken equal to b):
Beauvais Theoretical Biology and Medical Modelling (2017) 14:12 Page 11 of 17
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aaþbbðÞ
2¼aaðÞ
2þbbðÞ
2þ2abðÞ
2¼1ð16Þ
aaþbbðÞ
2þbaabðÞ
2¼aaðÞ
2þbbðÞ
2þbaðÞ
2þabðÞ
2¼1ð17Þ
1þ0¼1=2þ1=2¼1ð18Þ
As can be seen in Fig. 7, the left-hand side of Eq. (17) is the sum of Prob (direct) plus
Prob (reverse) without a remote supervisor and the right-hand side is the sum of Prob
(direct) plus Prob (reverse) with a remote supervisor. The terms aand bare thus
probability amplitudes and their squaring allows calculating the corresponding
probabilities.
Therefore, the probability of a direct relationship without a remote supervisor is cal-
culated by doing the sum of the probability amplitudes of the two paths that lead to a
direct relationship and then by squaring this sum. With a remote supervisor, the prob-
ability of a direct relationship is calculated by squaring the probability amplitude of
each path that leads to a direct relationship and then by making the sum of the prob-
abilities of the two paths (Fig. 7).
The relationship between labels and biological outcomes in the modeling has the
same logic as single-photon self-interferences in Youngs double-slit experiment where
photons behave either as particles when paths are detected or as waves when paths are
not detected. In Fig. 7 that sketches an elementary experiment, quantum-like correla-
tions are observed when paths(i.e. labels) are undistinguishable (from an outside
standpoint) and correlations vanish when they are distinguishable for a remote super-
visor. In this last case, each label is forced to adopt a defined pathway.
The emergence of quantum-like correlations is the consequence of the initial as-
sumptions, namely the independent probabilistic expectations and the intersubjective
agreement. The concomitant consideration of these two assumptions implies that the
outcome of an experiment does not pre-exist to the interaction of Oand Ofrom the
standpoint of P. This is a characteristic of quantum measurements and, in the language
of quantum mechanics, the stateof Oconcerning his identification of the outcome
Fig. 7 Probability of a direct relationship without or with a remote supervisor. The quantum-like probability
of a direct relationship is calculated as the square of the sum of the probability amplitudes of the different
possible paths. With a remote supervisor, classical probability applies and the probability of a direct
relationship is calculated as the sum of squares of the probability amplitudes of the paths. Therefore, the
probabilities of a direct relationship are different without or with a remote supervisor
Beauvais Theoretical Biology and Medical Modelling (2017) 14:12 Page 12 of 17
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
would be said superposedbefore interacting with O(and vice versa). The intersub-
jective agreement plays a similar role as a conservative law in physics and Oand O
would be said entangledafter their interaction.
Importance of an uninvolved standpoint
The uninvolved standpoint of the participant Pis central in the construction of the
modeling. Indeed, from the standpoint of O, if he observes a direct relationship or a re-
verse relationship, then he can hold for sure that Owill tell him that he observes the
same event. As a consequence the probability that Oand Oobserve a direct relation-
ship is pin this case as stated by classical probability and not p×p(before
renormalization) from the standpoint of P. The standpoints of Pand O-Ocoincide in
situations where these two equations are verified:
p¼p2
p2þq2and q¼q2
p2þq2ð19Þ
These two equations are equivalent to (2p1) (p1) = 0 and (2q1) (q1) = 0, re-
spectively. Therefore, there are only three possible values for p: 1/2, 1 or 0. These
values are the probabilities associated with initial position, stable positions #1 and #2,
respectively. Only the outside standpoint of Pwho is not involved in the observation of
the experiment allows describing the transition of Prob (direct) from 1/2 to 1 (or 0) as
a consequence of the emergence of quantum-like interferences(i.e. the cross-terms
with probability amplitudes equal to band -b in Fig. 7).
The differences between the standpoints of O-Oand Pare the consequence of the
demonstration of Breuer about the impossibility of a complete self-measurement [16].
According to this demonstration, a measurement apparatus (or an observer) is unable
to distinguish all the states of a system in which it is contained (whether this system is
classical or quantum mechanical does not matter). Only a second external apparatus
(P) that observes both the first apparatus (O) and the system (S) is able to account all
correlations between Oand S[17].
Optimized placebos in clinical trials
Without any doubt, the success of many complementary or alternative medicines rests
on placebo effect. Thus, most authors consider homeopathy as a perfect illustration of
the enforcement of the placebo effect in medicine. Moreover, homeopathic medicines
could be considered as super placebos(or optimized placebos) since even practi-
tioners think that they prescribe truemedicines despite the absence of active mole-
cules. Indeed, the manufacturing process of a majority of homeopathic medicines
eliminates the initial active molecules by serially diluting them well beyond the limit set
by Avogadros number. In other words, there are zero active molecules in these highly
diluted samples. Even if tiny traces of the initial molecules would be present (due to
contamination or imperfect diluting process), it remains to demonstrate how they
could nevertheless have an effect contradicting the law of mass action.
Since no classical pharmacological action can be assigned to high dilutions, it has
been suggested that modifications of water structure during the dilution process could
account for the alleged effects. Until now, no convincing evidence has been reported
indicating that modifications of water structure specific of the initial molecules are able
Beauvais Theoretical Biology and Medical Modelling (2017) 14:12 Page 13 of 17
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
to induce specific biologic changes. Moreover, homeopathy medicines available in phar-
macies are sugar granules that have been impregnated with high dilutions and then
dried. Therefore, until there is evidence to the contrary, the most reasonable scientific
attitude is to consider homeopathy medicines and high dilutions as plain placebos.
Interestingly, the gold standard for drug evaluation, namely blind randomized clinical
trial, appears to be an obstacle in studies aimed to establish the efficacy of homeopathy
medicines. Thus, the study of Shang et al. compared homeopathy trials and matched
conventional-medicine trials [18, 19]. The authors concluded that homeopathy medi-
cines were comparable to placebos. Indeed, in contrast with conventional medicines,
double-blind design was associated with a strong decrease of the probability of success
when compared with open-label design. Although this study has been heavily criticized
by proponents of homeopathy, most of them nevertheless acknowledge that blind ran-
domized clinical trials are not adequate for assessing homeopathy medicines [20, 21]. A
randomized clinical trial by Brien et al. in patients with rheumatoid arthritis suggested
that homeopathy consultations, but not homeopathy medicines, were associated with a
clinical benefit thus reinforcing the idea of a placebo effect [22].
In 2013, I proposed a slight modification of trial design in order to increase the
chance to observe a difference between outcomes in double-blind placebo-controlled
randomized trials of homeopathy medicines. This suggestion was not an encourage-
ment for the practice of homeopathy, but an attempt to understand the persisting suc-
cess of this alternative medicine in the absence of a rational basis. Based on the
hypothesis that quantum-like correlations were responsible for successfulopen-label
homeopathy clinical trials, it was proposed to replace the centralized assessment of effi-
cacy in blind trials (generally done by statisticians) with a local assessment (by physi-
cians) [23]. Thieves et al. recently challenged this hypothesis and reported experiments
in a plant model (wheat germination) that compared a homeopathy medicine and a pla-
cebo both in local and centralized blind designs [24]. The results were in favor of the
initial hypothesis since a significant difference of plant growth was observed between
homeopathy medicine and placebo with local assessment while there was no significant
difference with centralized assessment. The interaction test for local vs. centralized
blind designs was statistically significant (p = 0.003). If we consider all samples (includ-
ing homeopathy medicine) as plain placebos that differ only by their labels, these re-
sults are in favor of the present hypothetical modeling. These results should be also an
encouragement for physicians to implement the same local blind design in clinical trials
comparing a placebo with homeopathy medicine (i.e. a second placebo) in order to test
in vivo the hypothesis of quantum-like correlations as depicted in Fig. 5.
Discussion
It is generally thought that the macroscopic world escapes to the consequences of
quantum physics due to the decoherence process. As a consequence, biological systems
are considered to behave only classically. Nevertheless, some phenomena such as
photosynthetic light harvesting or avian magnetoreception have been recently sug-
gested to be the consequence of quantum phenomena [25]. Asano et al. evidenced
quantum-like probabilistic behavior in Escherichia coli lactose-glucose metabolism [26].
In experimental psychology, some processes of cognition appear to obey to nonclassical
logic [27]. Thus, the purpose of the new field named "quantum cognitionis to describe
Beauvais Theoretical Biology and Medical Modelling (2017) 14:12 Page 14 of 17
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
cognitive processes such as reasoning, decision making, judgment, language, memory
or perception with mathematical quantum tools [2831]. Moreover, Aerts described
some experimental situations in physics where macroscopic devices could exhibit a
quantum-like behavior [32]. Interestingly, Aerts showed that quantum probabilities
could be introduced as the consequence of a lack of knowledge about fluctuations dur-
ing the interaction between a measuring device and the object to be measured [32].
Most authors that use quantum probability outside the field of physics do not consider
that the systems they describe are really quantum. Tools of quantum probability are
simply used to describe results that until then were considered paradoxical [27]. In-
deed, quantum physics is not only a new mechanics but also a new probability theory.
An extension of classical probability with some mathematical tools borrowed to
quantum probability (e.g. superposition, entanglement, interferences) appears to be
fruitful in these different domains. With the present hypothetical modeling, it is pro-
posed that quantum-like correlations could be a component of the placebo effect.
A central question is the generalisability of the proposed modeling to other experi-
mental situations. Indeed, one could argue that bets on a coin toss could be also de-
scribed by the same modeling by replacing labels with bets and biological system with
coin toss. The answer is in Eq. (6) that supposes first that the system Shas an internal
structure submitted to small random fluctuations (thermal fluctuations for example)
and second that each p
n+1
value is strongly dependent on p
n
value. In other words,
probabilities p
n+1
are correlated with probabilities p
n
. This last characteristic is named
temporal autocorrelation and is a feature of phenomena with slow random fluctuations
such as systems submitted to Brownian motion or biological systems. Of course, an-
other implicit condition is the absence of physical obstacles that would block the transi-
tion of Prob (direct). Therefore, for systems based on a phenomenon not submitted to
internal fluctuations (radioactive decay) or rigidsystems with sufficient mechanical
inertia to be not influenced (coin flipping or dice rolling), εis equal to zero and no
transition is possible. For experimental systems submitted to internal fluctuations, but
with successive states that are not autocorrelated due to strong restoring forces
(elasticsystems), a transition as described in Fig. 4 is not possible (only random fluc-
tuations around 1/2 are observed). An example of such a system is a beam splitter that
randomly transmits or reflects a photon and vibrates around a fixed point. Systems
based on phenomena with large random fluctuations (electronic noise for example) are
also unsuitable.
The possibility to be experimentally tested is the hallmark of a scientific theory.
The proposed modeling predicts that quantum-like correlations vanish when they
are assessed by a remote supervisor. Only local assessments allow quantum-like
interferenceswith correlation of expectedand observed outcomes. It is import-
ant to emphasize that this modeling does not describe a causal relationship be-
tween mental states (e.g. intention) and physical states. Indeed, only quantum-like
correlations are allowed and there is no way to transmit messages, instructions or
orders from a laboratory to another one by using a series of coded samples.
Walach has extensively studied the relationship between homeopathy and notions
from quantum logic such as complementarity and entanglement by using a generalized
quantum theory[33, 34]. Of interest, this author insisted that homeopathy medicines
and their associated clinical outcomes could not be treated causally (as it the case in
Beauvais Theoretical Biology and Medical Modelling (2017) 14:12 Page 15 of 17
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
blind randomized clinical trials), otherwise mismatches between outcomes occurred
[35]. The present modeling with two placebo, which are differently labeled, leads to the
same conclusion. Moreover, it is not excluded that quantum-like correlations could
emerge in clinical trials for conventional drugs and add to classical causal relationship.
Some authors reported clinical trials where placebos associated with different labels
or therapeutical rituals could lead to different outcomes [36, 37]. Only psychological
mechanisms were supposed to be the cause of the different outcomes. Nevertheless, it
would be interesting to evaluate a possible involvement of quantum-like correlations in
such experiments aimed at investigating the placebo effect.
The potential existence of quantum-like correlations in the context of the experi-
menter effect could be also an element interesting to explore in the current debate
about low reproducibility in life sciences [38]. Indeed, differences among experimenters
teams are expected for the establishment of quantum correlations according to the
modeling. As a matter of fact, trials in biology, medicine or psychology could benefit
from an extended theory of probability that permits interferences between probabilities
(more exactly between probability amplitudes).
Conclusion
The hypothetical modeling proposed in this article suggests that two placebos with dif-
ferent labels can be associated with different outcomes even in blind trials. Such a
counterintuitive conclusion is the consequence of a probabilistic modeling that autho-
rizes quantum-like interferences. This modeling could give a framework for some unex-
plained observations where mere placebos are compared (in some alternative
medicines for example) and could be tested in blind trials by comparing local vs. re-
mote assessment of correlations.
Acknowledgements
Not applicable.
Funding
No funding
Availability of data and material
Not applicable.
Authorscontributions
Not applicable (unique author)
Competing interests
The author declares that he has no competing interests
Consent for publication
Not applicable.
Ethics approval and consent to participate
Not applicable.
PublishersNote
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Received: 15 February 2017 Accepted: 25 May 2017
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2.
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... In order to mitigate and possibly detect the phenomena mimicking a placebo effect (59), one proposed methodological approach is to include a "no treatment" arm, in which "no treatment" is administered, as part of a "three-arms trial" (60,61), comprising a real intervention, a sham control, and the additional no-intervention control group (42,62,63). . Although this is seldomly used (64)(65)(66), including a "no-treatment" arm could not only detect the causal effect of the placebo (39,(67)(68)(69)(70)(71)(72) but also allow for estimating a more precise effect of the treatment and placebo (54,65,66). Three distinct types of no-treatment groups have been used: 1) Non-manual, non-specific control group: a 'hands-off' group in which participants are exposed to all aspects of the research paradigm (i.e., setting, patient-clinician contact) without being touched (40), thus preserving all non-manual, non-specific elements of placebo. ...
... In order to mitigate and possibly detect the phenomena mimicking a placebo effect (59), one proposed methodological approach is to include a "no treatment" arm, in which "no treatment" is administered, as part of a "three-arms trial" (60,61), comprising a real intervention, a sham control, and the additional no-intervention control group (42,62,63). . Although this is seldomly used (64)(65)(66), including a "no-treatment" arm could not only detect the causal effect of the placebo (39,(67)(68)(69)(70)(71)(72) but also allow for estimating a more precise effect of the treatment and placebo (54,65,66). Three distinct types of no-treatment groups have been used: 1) Non-manual, non-specific control group: a 'hands-off' group in which participants are exposed to all aspects of the research paradigm (i.e., setting, patient-clinician contact) without being touched (40), thus preserving all non-manual, non-specific elements of placebo. ...
Article
Full-text available
Randomised placebo-controlled trials are implemented to determine whether a particular therapy is superior to placebo and can thus be considered, effective. However, adopting the standard RCT design in contexts other than pharmacological trials, such as manual therapy, may result in systematic biases. These biases may occur due to: the impossibility of traditional “double-blinding” in manual therapy trials; insufficient pre-training of operators delivering the treatment and/or sham therapy; biased recruitment of study participants; the problematic use of subjective and/or objective outcomes; and finally, the presence of phenomena mimicking placebo effects. From the perspective of placebo studies, the purpose of this paper is to discuss and make appropriate recommendations to address these five issues in manual therapy research.
... It is worth noting that the placebo effect is considered more relevant in non-pharmacological treatments [20,21] including complementary alternative medicines (CAMs) [20,22]. It depends on several conditions, including the significant role of interpersonal touch [9], the multiplicity of treatment sessions [23], and the optimisation of the patient-physician relationship . ...
... Page 12 of 14 Giandomenico et al. BMC Medical Research Methodology (2022) 22:219 These Terms are supplementary and will apply in addition to any applicable website terms and conditions, a relevant site licence or a personal subscription. These Terms will prevail over any conflict or ambiguity with regards to the relevant terms, a site licence or a personal subscription (to the extent of the conflict or ambiguity only). ...
Article
Full-text available
Background To measure the specific effectiveness of a given treatment in a randomised controlled trial, the intervention and control groups have to be similar in all factors not distinctive to the experimental treatment. The similarity of these non-specific factors can be defined as an equality assumption. The purpose of this review was to evaluate the equality assumptions in manual therapy trials. Methods Relevant studies were identified through the following databases: EMBASE, MEDLINE, SCOPUS, WEB OF SCIENCE, Scholar Google, clinicaltrial.gov, the Cochrane Library, chiloras/MANTIS, PubMed Europe, Allied and Complementary Medicine (AMED), Physiotherapy Evidence Database (PEDro) and Sciencedirect. Studies investigating the effect of any manual intervention compared to at least one type of manual control were included. Data extraction and qualitative assessment were carried out independently by four reviewers, and the summary of results was reported following the PRISMA statement. Result Out of 108,903 retrieved studies, 311, enrolling a total of 17,308 patients, were included and divided into eight manual therapy trials categories. Equality assumption elements were grouped in three macro areas: patient-related, context-related and practitioner-related items. Results showed good quality in the reporting of context-related equality assumption items, potentially because largely included in pre-existent guidelines. There was a general lack of attention to the patient- and practitioner-related equality assumption items. Conclusion Our results showed that the similarity between experimental and sham interventions is limited, affecting, therefore, the strength of the evidence. Based on the results, methodological aspects for planning future trials were discussed and recommendations to control for equality assumption were provided.
... A new approach considering not only the "biological systems" (patients), but also the various "experimenters" and participants (physicians, patients, statisticians, etc) could be fruitful. Similarly, studies on placebo effect could also benefit from this original perspective if the "meaning" of the medicines -for both patients and physicians -is also considered [39,40]. ...
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Background: Benveniste’s biology experiments suggested the existence of molecular-like effects without molecules (“memory of water”). In this article, it is proposed that these disputed experiments could have been the consequence of a previously unnoticed and non-conventional experimenter effect. Methods: A probabilistic modelling is built in order to describe an elementary laboratory experiment. A biological system is modelled with two possible states (“resting” and “activated”) and exposed to two experimental conditions labelled “control” and “test”, but both biologically inactive. The modelling takes into account not only the biological system, but also the experimenters. In addition, an outsider standpoint is adopted to describe the experimental situation. Results: A classical approach suggests that, after experiment completion, the “control” and “test” labels of biologically-inactive conditions should be both associated with “resting” state (i.e. no significant relationship between labels and system states). However, if the fluctuations of the biological system are also considered, a quantum-like relationship emerges and connects labels and system states (analogous to a biological “effect” without molecules). Conclusions: No hypotheses about water properties or other exotic explanations are needed to describe Benveniste’s experiments, including their unusual features. This modelling could be extended to other experimental situations in biology, medicine and psychology.
... Alternative medicines such as homeopathy or placebo effect are examples where this model could be applied. 32 As depicted in this article, the structuration of the observer's mind by classical conditioning could organize the observations and measurements. In such a situation, the experimenters are trapped into a circular process: they describe what they contribute to construct and they construct what contributes to their description. ...
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The “memory of water” experiments suggested the existence of molecular-like effects without molecules. Although no convincing evidence of modifications of water – specific of biologically-active molecules – has been reported up to now, consistent changes of biological systems were nevertheless recorded. We propose an alternate explanation based on classical conditioning of the experimenter. Using a probabilistic model, we describe not only the biological system, but also the experimenter engaged in an elementary dose-response experiment. We assume that during conventional experiments involving genuine biologically-active molecules, the experimenter is involuntarily conditioned to expect a pattern, namely a relationship between descriptions (or “labels”) of experimental conditions and corresponding biological system states. The model predicts that the conditioned experimenter could continue to record the learned pattern even in the absence of the initial cause, namely the biologically-active molecules. The phenomenon is self-sustained because the observation of the expected pattern reinforces the initial conditioning. A necessary requirement is the use of a system submitted to random fluctuations with autocorrelated successive states (no forced return to the initial position). The relationship recorded by the conditioned experimenter is, however, not causal in this model because blind experiments with an “outside” supervisor lead to a loss of correlations (i.e., system states randomly associated to “labels”). In conclusion, this psychophysical model allows explaining the results of “memory of water” experiments without referring to water or another local cause. It could be extended to other scientific fields in biology, medicine and psychology when suspecting an experimenter effect.
... A new approach considering not only the "biological systems" (patients), but also the various "experimenters" and participants (physicians, patients, statisticians, etc.) could be fruitful. Similarly, studies on the placebo effect could also benefit from this original perspective if the "meaning" of the medicines-for both patients and physicians-is also considered [43,44]. ...
Article
Full-text available
Background: Benveniste's biology experiments suggested the existence of molecular-like effects without molecules ("memory of water"). In this article, it is proposed that these disputed experiments could have been the consequence of a previously unnoticed and non-conventional experimenter effect.Methods:A probabilistic modelling is built in order to describe an elementary laboratory experiment. A biological system is modelled with two possible states ("resting" and "activated") and exposed to two experimental conditions labelled "control" and "test", but both are biologically inactive. The modelling takes into account not only the biological system, but also the experimenters. In addition, an outsider standpoint is adopted to describe the experimental situation.Results:A classical approach suggests that, after experiment completion, the "control" and "test" labels of biologically-inactive conditions should both be associated with the "resting" state (i.e., no significant relationship between labels and system states). However, if the fluctuations of the biological system are also considered, a quantum-like relationship emerges and connects labels and system states (analogous to a biological "effect" without molecules).Conclusions:No hypotheses about water properties or other exotic explanations are needed to describe Benveniste's experiments, including their unusual features. This modelling could be extended to other experimental situations in biology, medicine, and psychology.
... A new approach considering not only the "biological systems" (patients), but also the various "experimenters" and participants (physicians, patients, statisticians, etc) could be fruitful. Similarly, studies on placebo effect could also benefit from this original perspective if the "meaning" of the medicines -for both patients and physicians -is also considered [13,14]. ...
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Full-text available
Background. In experimental sciences, conception of an experiment and record of the outcomes must be strictly separated. Although many possible pitfalls have been described, particularly in biological sciences, one cannot exclude unknown loopholes. Methods. A simple probabilistic modeling is constructed in order to describe experimenters testing the hypothesis of a relationship between some experimental conditions (supposed causes) and states of a biological system (observed effects). The modeling rests on two preliminary remarks. First, after assessment of a relationship, the outcome is not a property of the system alone, but is a property of the experimenters and the system taken as a whole. Second, as a consequence, the outcome does not preexist to measurement. Results. A biological system with two possible states ("resting" and "activated") exposed to two control conditions distinguished only by their "labels" is modeled. A classical approach suggests that the two control conditions are both associated with the "resting" state (i.e. no relationship). Nevertheless, if the fluctuations of the system are considered, the hypothesis of a significant relationship between "labels" and system states is confirmed. In contrast, if the outcomes are not globally recognized as a relationship, but remains unconnected by the experimenters, no significant relationship emerges. Conclusion. This probabilistic modeling suggests that, despite precautions, the strict separation of biological systems and experimenters is an ideal not necessarily achieved when the hypothesis of a relationship is tested. The consequences could be wrong conclusions about causal relationships. Specific blind procedures are proposed to prevent unwanted correlations involving the experimenters.
... A new approach considering not only the "biological systems" (patients), but also the various "experimenters" and participants (physicians, patients, statisticians, etc) could be fruitful. Similarly, studies on placebo effect could also benefit from this original perspective if the "meaning" of the medicines -for both patients and physicians -is also considered [13,14]. ...
Preprint
Background. In experimental sciences, conception of an experiment and record of the outcomes must be strictly separated. Although many possible pitfalls have been described, particularly in biological sciences, one cannot exclude unknown loopholes. Methods. A simple probabilistic modeling is constructed in order to describe experimenters testing the hypothesis of a relationship between some experimental conditions (supposed causes) and states of a biological system (observed effects). The modeling rests on two preliminary remarks. First, after assessment of a relationship, the outcome is not a property of the system alone, but is a property of the experimenters and the system taken as a whole. Second, as a consequence, the outcome does not preexist to measurement. Results. A biological system with two possible states (“resting” and “activated”) exposed to two control conditions distinguished only by their “labels” is modeled. A classical approach suggests that the two control conditions are both associated with the “resting” state (i.e. no relationship). Nevertheless, if the fluctuations of the system are considered, the hypothesis of a significant relationship between “labels” and system states is confirmed. In contrast, if the outcomes are not globally recognized as a relationship, but remains unconnected by the experimenters, no significant relationship emerges. Conclusion. This probabilistic modeling suggests that, despite precautions, the strict separation of biological systems and experimenters is an ideal not necessarily achieved when the hypothesis of a relationship is tested. The consequences could be wrong conclusions about causal relationships. Specific blind procedures are proposed to prevent unwanted correlations involving the experimenters.
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